Abstract
It has been shown that the inclusion of an isolated class in the classical SIR model for childhood diseases can be responsible for self-sustained oscillations. Hence, the recurrent outbreaks of such diseases can be caused by autonomous, deterministic factors. We extend the model to include a latent class (i.e. individuals who are infected with the disease, but are not yet able to pass the disease to others) and study the resulting dynamics. The existence of Hopf bifurcations is shown for the model, as well as a homoclinic bifurcation for a perturbation to the model. For historical data on scarlet fever in England, our model agrees with the epidemiological data much more closely than the model without the latent class. For other childhood diseases, our model suggests that isolation is unlikely to be a major factor in sustained oscillations.
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Gerberry, D.J., Milner, F.A. An SEIQR model for childhood diseases. J. Math. Biol. 59, 535–561 (2009). https://doi.org/10.1007/s00285-008-0239-2
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DOI: https://doi.org/10.1007/s00285-008-0239-2